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6 results for “PCA”

1. Machine Learning · Lesson

   PCA = Eigenvectors of Covariance

   PCA = Eigenvectors of Covariance | Machine Learning | MathAtlas Principal components are eigenvectors of the covariance matrix Σ = (1/n) Xᵀ X — equivalently the right singular vectors of the centered data.

2. Random Matrices · Lesson

   Beyond the Semicircle

   Covariance matrices, the noise floor of PCA, and eigenvalues that fill a disc

3. Machine Learning · Lesson

   Kernels & Feature Spaces

   … algorithm that touches its inputs only through inner products (linear regression, SVMs, PCA, ridge regression) can be run inside the lifted feature space without ever computing φ.

4. Machine Learning · Module overview

   Machine Learning

   Loss surfaces and gradient descent, PCA as an eigendecomposition, kernels as inner products in implicit Hilbert spaces, backprop as the chain rule, Bayesian updating, cross-entropy, equivariant convolutions, and the manifold hypothesis — all visualized.

5. Random Matrices · Module overview

   Random Matrices

   … computed live from the Hardy Z function The Marchenko-Pastur noise floor behind PCA Random Matrix Theory | MathAtlas Interactive exploration of random matrix theory — the Wigner semicircle law, eigenvalue repulsion, the Tracy–Widom distribution, universality, and the unexplained agreement between the Riemann zeta zeros …

6. Machine Learning · Lesson

   The Manifold Hypothesis

   PCA, t-SNE, UMAP, and autoencoders unfold it.